The scientific challenges of laser-ranged satellites

The LAGEOS (LAser GEOdynamics Satellite) and LARES (LAser RElativity Satellite) geodetic satellites have been instrumental also in probing fundamental physics and testing gravitational theories in the weak-field and slow-motion limit of General Relativity (GR). This review paper summarizes key scientific challenges and achievements, focusing on the Precise Orbit Determination (POD) of these passive satellites, the accurate modeling of non-gravitational perturbations, and the subsequent use of orbital residuals to constrain post-Newtonian parameters and alternative theories of gravity. We detail the advanced modeling techniques for spin dynamics, neutral drag, and thermal thrust effects, crucial for achieving millimeter-level precision in orbit. The core of the analysis relies on excluding GR effects from the dynamical models during POD, thus preserving relativistic signatures in the orbital residuals. The paper highlights significant results from the LARASE and SaToR-G projects, including precise measurements of the Schwarzschild and Lense-Thirring precessions. These measurements have yielded stringent constraints on combinations of PPN parameters, non-symmetric gravitation theories, torsional theories, and Yukawa-like long-range interactions, considerably advancing our understanding of gravitational physics beyond GR’s predictions. Future directions include leveraging the mean anomaly as an additional observable and exploring violations of Local Lorentz Invariance to further refine these tests.